Classifying Integrable Egoroff Hydrodynamic Chains

We introduce the notion of Egoroff hydrodynamic chains. We show how they are related to integrable (2+1)-dimensional equations of hydrodynamic type. We classify these equations in the simplest case. We find (2+1)-dimensional equations that are not just generalizations of the already known Khokhlov–Zabolotskaya and Boyer–Finley equations but are much more involved. These equations are parameterized by theta functions and by solutions of the Chazy equations. We obtain analogues of the dispersionless Hirota equations.     

Rank one lattices whose parabolic isometries have no rotational part

We prove a result on certain finite index subgroups of rank one lattices which is motivated by cusp closing constructions.

     

The effect of topological fluctuations on the heat capacity of superconductor

The effect of topological excitations in the form of small size (r ≪ξ(T)) vortex rings on thermodynamics of a bulk superconductor is considered. These specific short wavelength fluctuations of the order parameter are analogous to small vortex-antivortex pairs in superconducting film which were recently studied in Y.N. Ovchinnikov, A.A. Varlamov, Phys. Rev. Lett. 94, 107007 (2004). The corresponding contribution to the free energy below T_c is calculated. It is shown that fluctuations of this type give the main temperature dependent contribution to the heat capacity of the superconductor in the sufficiently large interval of temperatures below the transition point. Important, that the sign of this contribution is opposite to that one appearing due to the usual long wavelength fluctuation, leading to smearing of the BCS jump of heat capacity.     

Generalized Alexandroff Duplicates and CD 0(K) spaces

We define and investigateCD _Σ,Γ(K, E)-type spaces, which generalizeCD ₀-type Banach lattices introduced in [1]. We state that the space CD _Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8].     

Activation energy in La0.7Ca0.3MnO3/YBa2Cu3O7-δ / La0.7Ca0.3MnO3 superconducting trilayers

Resistivity vs. temperature measurements on La_0.7Ca_0.3MnO₃/YBa₂Cu₃O_7-δ /La_0.7Ca_0.3MnO₃ (LCMO/YBCO/LCMO) trilayers with different YBCO thickness, were performed in external magnetic field H up to 8 T. By evaluating the activation energy U from the slope of the resistivity Arrhenius plot, a strong depression of U has been observed when decreasing the YBCO layer thickness and the absolute U values appear to be reduced with respect to the values reported in literature in the case of YBCO thin films and YBCO/insulating multilayers. Moreover, a logarithmic U vs. H dependence is shown both in the case of thick and thin YBCO layers indicating the formation of a two dimensional vortex lattice. The experimental data are discussed considering the strong influence of the ferromagnetic LCMO on the superconducting YBCO properties which reduces the effective YBCO thickness more than predicted by the conventional theories.     

市-县有线数字电视传输系统浅析

针对地市建设有线数字电视统一服务平台的要求，对通过DS3接口传输、ATM over SDH，ASI接口传输，QAM调制等几种有线数字电视传输方法进行可行性探讨。     

Bands in lattices of operators

We consider the lattice of regular operators on a Dedekind complete Banach lattice. We show that in general the projection onto a band generated by a lattice homomorphism need not be continuous and that the principal bands need not be closed for the operator norm. In fact it is possible to find a convergent sequence of operators all the members of which are disjoint from the limit.

     

数字CATV系统主要技术浅析

鉴于目前各地有线网络正在全面推广数字电视 ,掌握和推动数字电视的发展已十分重要。对有线数字系统的工作原理、系统各主要技术作分析 ,以便在实际工作中正确应用。     

Control of a coupled map lattice model for vortex shedding in the wake of a cylinder

The flow behind a vibrating flexible cable at low Reynolds numbers can exhibit complex wake structures such as lace-like patterns, vortex dislocations and frequency cells. These structures have been observed in experiments and numerical simulations, and are predicted by a previously developed low-order coupled map lattice (CML). The discrete (in time and space) CML models consist of a series of diffusively coupled circle map oscillators along the cable span. Motivated by a desire to modify the complex wake patterns behind flexible vibrating cables we have studied the addition of control terms into the highly efficient CML models and explored the resulting dynamics. Proportional, adaptive proportional and discontinuous non-linear (DNL) control methods were used to derive the control laws. The first method employed occasional proportional feedback. The adaptive method used spatio-temporal feedback control. The DNL method used a discontinuous feedback linearization procedure, and the controller was designed for the resulting linearized system using eigenvalue assignment. These techniques were applied to a modeled vortex dislocation structure in the wake of a vibrating cable in uniform freestream flow. Parallel shedding patterns were achieved for a range of forcing frequency-forcing amplitude combinations studied to validate the control theory. The adaptive proportional and DNL methods were found to be more effective than the proportional control method due to the incorporation of a spatially varying feedback gain across the cylinder span. The DNL method was found to be the most efficient controller of the low-order CML model. The required control level across the cable span was correlated to the 1/1 lock-on behavior of the temporal circle map.